Question

An analyst is preparing a report for the CEO of a company. Two options for insurance, A and B, are available for purchase by the company. There is an 80% chance an incident will be covered with option A and 95% chance an incident will be covered if option B is used. Option B is more expensive, however, and the analyst estimates only a 30% chance the CEO will select it (the CEO will select option A the other 70% of the time).

Use the following notation:

A— option A is purchased
B— option B is purchased
C— a given incident is covered

Q

Which of the following is the correct representation of the information that is provided to us?

P(A) = .70, P(B) = .30, P(C|A) = .80, P(C|B) = .95

P(A|C) = .70, P(B|C) = .30, P(C|A) = .80, P(C|B) =.95

P(A and C) = .70, P(B and C) = .30, P(C|A) = .80, P(C|B) = .95

P(A) = .70, P(B) = .30, P(A|C) = .80, P(B|C) = .95

P(A) = .70, P(B) = .30, P(A and C) = .80, P(B and C) =.95

Q

What is the probability that an incident will be covered?

P(C) = .70 * .80 + .30 * .95 = .845

P(C) = .30 * .95 = .2375

P(C) = .70 * .80 = .56

P(C) = .70 * .95 + .30 * .80 = .905

P(C) = .70 * .30 + .80 * .95 = .97

Q

A particular incident was covered. What is the probability that the CEO chose to purchase option A?

(0.70 * 0.80) / (0.70*0.80 + 0.30*0.95) = 0.66272

(0.70 * 0.80) / (0.80 + 0.95) = 0.32

(0.30 * 0.95) / (0.70*0.80 + 0.30*0.95) = 0.33728

0.70 * 0.80 = 0.56

0.80

Answer 1

Answer - 1: The correct given values are:

P(A) = .70, P(B) = .30, P(C|A) = .80, P(C|B) = .95

Option A is correct.

Answer - 2: P(C) = .70 * .80 + .30 * .95 = .845

Option A is correct.

Answer - 3: P(CEO to purchase option A) = (0.70 * 0.80) / (0.70*0.80 + 0.30*0.95) = 0.66272

Option A is correct.